L24 Math 318 (Calculus of Several Variables) Syllabus
This is the class webpage and syllabus for Math 318 in Spring 2019. Any changes or updates to the syllabus will be posted here and will be announced in class.
- Instructor: Dr. Tyler Bongers, email@example.com
- Office hours: 1-3 PM Tuesday; 1-2 PM Wednesday; 11AM-12PM Friday; Cupples I 203.
If none of these times work for you, you can find additional hours at YouCanBook.me.
- Course location and times: Cupples II L009, MWF 9-9:50 (Section 01); Crow 204, MWF 12-12:50 (Section 02).
Selected topics for functions of several variables involving some matrix algebra and presented at a level of rigor intermediate between that of Calculus III and higher level analysis courses. Students may not receive credit toward a mathematics major or minor for both Math 308 and 318. Prerequisites: Math 233 and Math 309 (not concurrent).
The textbook for the course is Calculus of Several Variables by Brian E. Blank. It is available as a free pdf posted on Canvas; you are welcome to print out as much of the text as you would like. However, in accordance with the author's wishes, the textbook may not be redistributed. In particular, do not post the book online.
This course approaches derivatives and integrals in a more in-depth manner than Math 233, and uses the tools of linear algebra developed in Math 309 to use, calculate, and interpret the objects. The course assumes familiarity with partial derivatives, matrix computations, vector spaces, integration over regions in the plane and 3-space, and other material from the prerequisites. We will then use these ideas to develop a unified theory of differentiation and integration on manifolds, which are the natural spaces for doing calculus. This course will serve as a bridge between the computational calculus courses and the later analysis courses that you may encounter.
In particular, some of the main goals and objectives for the course are to gain familiarity and computational fluency with
- Treating derivatives of vector-valued functions with vector inputs as matrices
- Relate the rules of differentiation from the classical setting to their higher-dimensional analogues (e.g. the chain rule)
- Use the inverse and implicit function theorems to analyze implicitly defined functions and solution sets
- Use the language of point-set topology (open, closed, boundary, etc.) to describe regions in manifolds
- Describe manifolds in various ways, and understand how they generalize Euclidean spaces
- Describe form fields and calculate exterior derivatives
- Integrate form fields on manifolds, and understand the connections to Stokes' theorem and related theorems.
In addition to the specific content goals, you should also work on
- Problem-solving skills and applying concepts in new areas
- Abstraction and generalization from the classical settings
- Reading and using the textbook to explore concepts
- Communicating mathematics both verbally (e.g. with your peers in lecture) and in writing (e.g. on homework).
Homework, Exams, and Grading Scale
There will be two main kinds of evaluations during this course: weekly homeworks, and exams.
- Homework: Homework will be due roughly weekly, typically on Wednesdays, and will be submitted through Crowdmark. Each week, there will be three separate parts to submit: brief computations, fully written problems, and brief reflective writing assignments. On each of these, you are strongly encouraged to collaborate with each other and discuss the problems; however, your writeups must be done individually without copying. Please see the teaching and learning philosophy section for the full details on all of this, and the assessment standards for information about the grading policies.
Homework remediation policy: Your lowest homework score will be dropped automatically. Late homework submissions will still be accepted the next day, but will be subject to a 30% reduction in score.
- Exams: There will be two midterm exams (tentatively scheduled after we finish Chapter 2 and Chapter 4, respectively), as well as a computationally-focused quiz (tentatively scheduled after we finish Chapter 3). The final exam is from 8:30 pm to 10:30 pm on December 13. If something happens that prevents you from taking an exam, you must contact the instructor as early as possible to make alternative arrangements.
Exam remediation policy: If your score on the final exam exceeds your score on a midterm exam, then your final exam score will automatically replace the lowest midterm exam.
The points for the course will be distributed as follows:
| Homework || 25%
| Exam 1 || 15%
| Quiz || 10%
| Exam 2 || 15%
| Final Exam || 35%
Your final grade will be assigned given the cutoffs in the table below. Please note that scores will not be rounded - a 79.99% will still translate to a B, not a B+. If you are taking this as pass-fail, then the cutoff for a passing grade is C-. The grade of A+ will be given at the instructor's discretion.
| Grade || Points |
| A || ≥ 90% |
| A- || ≥ 85% |
| B+ || ≥ 80% |
| B || ≥ 75% |
| B- || ≥ 70% |
| C+ || ≥ 65% |
| C || ≥ 60% |
| C- || ≥ 55% |
| D || ≥ 50% |
| F || ≥ 0% |
Teaching and learning philosophy
There are a few core beliefs that guide my teaching, and which I hope you will find useful in your learning process:
- The best way to learn math is by doing math - this means actively engaging with the material, and striving with problems. Mathematics is not a passive science, but rather requires active work on the ideas. I strongly encourage you to do as many problems from the textbook as you can (and to only check the solutions after you've seriously tried them!).
- Another important skill is communicating math. This takes many forms: discussions with your peers in and out of lecture, the written notes and homeworks that you create, and the explanations that you have on exams. Following this idea, there will be a few key parts to each homework set: brief written computations (where you only need to write your calculations, as in previous courses); full-explanation problems, which must be written in complete sentences with full justification not only of your calculations but also why the approach is correct.
- It's also important to learn how to read and contextualize math. Reading a math textbook is very unlike the process of reading a novel or just about any other written material - it requires active engagement and work to understand the arguments and computations. As you read the book, you should take notes, write about your questions and their resolutions, and brainstorm ideas for how this material fits into the broader context of the math and science you've seen before. We will have guided reflections at the end of each homework assignment which are geared towards this process.
- Learning math is also a community activity. Work along side your classmates! If doing math is the best way to learn math, then teaching math is the second best way; finding an explanation for someone else, or having a discussion about a difficult concept, or just comparing notes on homework can lead to new ideas and insights. It's okay to make mistakes, and is a fundamental and natural part of learning.
Resources, support, and learning strategies
There are many resources available to help you succeed in the course - remember that we are here to help you get the most possible out of your time here! Here are some suggestions:
- Come to class. Not only will I talk about the day's material, there will be time for us to learn actively. Guided discussions and problem solving with your peers are great opportunities to learn (and explain your own knowledge to others), as well as to ask questions.
- Come to office hours. I have drop-in office hours scheduled throughout the week; talking about math is an important way of learning, and a brief discussion or picture might give you exactly the right idea to grasp a concept. If none of the standard times work for your schedule, please take a look at my YouCanBook.me page.
- Email me. If you have shorter questions about a concept, the homework or exams, or any other things that come up, please feel free to email me at firstname.lastname@example.org. I do my best to respond quickly (that is, within a few hours; almost surely by the end of the day) to emails that are sent before 8 pm during weekdays. However, I will generally be unavailable by email on Thursdays or weekends. I strongly encourage you to also schedule time off for yourself throughout the week, since mental health is such an important part of life; this brings us to...
- University resources. The university has numerous resources available for counseling and health and wellness.
- Calculators can be extremely helpful in developing visualizations and computational skills (or just for verification purpose). Although they will not be allowed on exams, you're encouraged to use them on homework to help explore the concepts. In particular, I recommend Sage and Octave as free and open-source software with visualization packages built in. Other alternatives include Matlab, Mathematica, and WolframAlpha.
- Finally, extra calculus support can also be found at the Calculus Help Room in Cupples I Room 8.
Other Course Policies and Helpful Information
- In the event that you cannot attend one of the required exams, please contact the instructor as soon as possible to make alternative arrangements. For arrangements in advance, you must contact me at least one week before the exam; in case of emergency (e.g. illness), contact me as soon as possible after the exam.
- Washington University is committed to providing accommodations and/or services to students with documented disabilities. Students who are seeking support for a disability or a suspected disability should contact Disability Resources at 935-4153. Disability Resources is responsible for approving all disability-related accommodations for WU students, and students are responsible for providing faculty members with formal documentation of their approved accommodations at least two weeks prior to using those accommodations. I will accept Disability Resources VISA forms by email and personal delivery. If you have already been approved for accommodations, I request that you provide me with a copy of your VISA within the first two weeks of the semester.
- Adherence to the university's academic integrity policy is expected and required. In particular, your homework submissions must be written up separately and individually - copying is never allowed, and will be treated as an act of plagiarism.